arXiv subjects
Publications and source records attributed to V. V. Fomichov.
In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval $[0;n]$ as $n\to\infty$ and obtain an estimate of the Berry-Esseen type for the rate of this convergence.
In this note we extend the main results of [2] and [8], which concern the weak convergence of the $n$-point motions of smooth Harris flows to those of the Arratia flow, to the case when the covariance functions of these Harris flows converge pointwise to a covariance function whose support is of zero Lebesgue measure.
In this paper we discuss the Wasserstein distance between the n-point motions of Harris flows whose covariance functions have compact support. We prove that it can be estimated by the diameters of their support provided the latter are sufficiently small.
In this paper we compute the level-crossing intensity for the density of the image of the Lebesgue measure under the action of a Brownian stochastic flow which is a smooth approximation of the Arratia flow and determine its asymptotic behaviour as the height of the level tends to infinity.
In this paper we consider the asymptotic behaviour of all moments of the interparticle distance and of all mixed moments of an isotropic Brownian stochastic flow which serves as a smooth approximation of the Arratia flow.